I am just reading a paper which uses the word “Identification” instead of equality. I think this has been proposed by Bob Harper. Can anybody enlighten me what is the difference between identifications and equality? Maybe there is an identification between them but they are not equal? Are the real numbers 0.999… identified or are they equal?
Thorsten
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I am tempted to add my grain of salt to this discussion.
I like the word "identification".
But what about "iso" ?
It means "equal". As in "iso-morphism", "iso-tope", etc.
https://wordinfo.info/unit/2795/page:9
Best,
André
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From: homotopyt...@googlegroups.com [homotopyt...@googlegroups.com] on behalf of Michael Shulman [shu...@sandiego.edu]
Sent: Monday, May 04, 2020 11:59 AM
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Cc: Thorsten Altenkirch; homotopyt...@googlegroups.com
Subject: Re: [HoTT] "Identifications" ?
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The term "iso" could be better.
Let f:a=b be an iso between the elements a and b of a type A.
Let f:A=B be an isomorphism between the types A and B.
The univalence principle state that every isomorphism is an iso.
A
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From: homotopyt...@googlegroups.com [homotopyt...@googlegroups.com] on behalf of Joyal, André [joyal...@uqam.ca]
Sent: Monday, May 04, 2020 12:16 PM
To: Michael Shulman; Stefan Monnier
Cc: Thorsten Altenkirch; homotopyt...@googlegroups.com
Subject: RE: [HoTT] "Identifications" ?
Dear all,
https://wordinfo.info/unit/2795/page:9
Best,
André
To view this discussion on the web visit https://groups.google.com/d/msgid/HomotopyTypeTheory/8C57894C7413F04A98DDF5629FEC90B1652F3F0F%40Pli.gst.uqam.ca.
The meanings of "equal" and "identical" are the same. They both mean "same", and are equivalent to "equivalent" according to most dictionaries.
Try not to be too judgmental, Thorsten.
Best,Martin
On Monday, 4 May 2020 10:35:53 UTC+1, Thorsten Altenkirch wrote:I am just reading a paper which uses the word “Identification” instead of equality. I think this has been proposed by Bob Harper. Can anybody enlighten me what is the difference between identifications and equality? Maybe there is an identification between them but they are not equal? Are the real numbers 0.999… identified or are they equal?
Thorsten
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